1. Field of the Invention
This invention relates to a refractive lens for focusing short wavelength X-rays.
2. Description of the Prior Art
It is well known that the complex refractive index n of a material can be expressed by EQU n=1-.delta.-i.beta. (1)
and that the following holds EQU 2.pi.(.delta.+i.beta.)=N.sub.a .multidot.r.sub.e .multidot..lambda..sup.2 .multidot.(f1+if2) (2)
where i: .sqroot.-1; .delta.: phase lag coefficient; .beta.: extinction coefficient; N.sub.a : atomic density; r.sub.e : classical electron radius; .lambda.: wavelength of light; and f1, f2: atomic scattering factors.
Reflecting mirrors and refractive lenses can easily be fabricated for use in the visible light region since materials having a refractive index n far from unity and a small absorption (.vertline..beta./.delta..vertline.&lt;1) in this region are readily available. In contrast, optical elements utilizing reflection or refraction are intrinsically difficult to fabricate for use in the X-ray region, since in this region all materials have a refractive index n near unity, i.e. .vertline..delta..vertline.&lt;1, and exhibit a large absorption.
Consider, for example, a concave piece of material having the shape of a paraboloid of revolution and satisfying the relationship EQU r.sup.2 =2.delta.f(d(r)-d0) (3)
where d(r) is the thickness at a distance r measured perpendicularly from the axis and d0 is the thickness at the thinnest portion, namely the portion through which the axis passes. In the case of a small coefficient .delta., such a concave piece of material functions as a lens which focuses a plane electromagnetic wave entering parallel to the axis at a focal distance of f. In the particular case where (d(r)-d0) is considerably smaller than r, Equation (3) can be approximated to a spherical surface of radius R, as shown by Equation (4) EQU R=.delta.f (4).
Since in the X-ray region .delta. generally has an extremely small absolute value on the order of 10.sup.-5, however, a lens fabricated according to Equation (4) would have a very long focal distance in the X-ray region. For instance, a concave lens fabricated of beryllium to have a radius of curvature R=1 cm would have a focal distance f of 4.5 Km with respect to X-rays of wavelength .lambda.=0.1 nm (such X-rays will hereinafter be referred to as 0.1 nm X-rays). Since the atomic scattering factor f1 of a material is approximately proportional to its atomic number Z, shorter focal distances can be obtained by using materials with larger atomic numbers Z. Still, even if gold (Z=79) is used, the focal distance is reduced to only around 220 m, or about 1/20th that of a beryllium lens.
Much work has gone into the development of techniques enabling the fabrication of X-ray optics. Among relatively early studies on refractive lenses is that published by P. Kirkpatrick (J.Opt.Soc.Am.39(1949)746). Kirkpatrick predicted that a linear focal pattern would be obtained when an 0.07 nm X-ray enters the concave side of an optical concave lens obliquely at an extremely shallow angle on the order of several .mu.rad. Since oblique incidence at an extremely shallow angle results in large aberration, however, the focusing characteristics obtained by this method are very poor and the absorption by the substrate is quite heavy. This is no doubt why no other studies on refractive X-ray lenses have been reported.
Focusing of X-rays has been attempted not by use of transmission lenses but by reflection techniques. When an electromagnetic wave is reflected at an interface where the refractive index is discontinuous, the reflection intensity increases with increasing difference in refractive index at the interface. In the X-ray region, however, where all materials exhibit a refractive index n near unity, the normal incident reflectance at a single interface is extremely small. This led to the idea of using a very shallow X-ray incidence angle for meeting the total reflection condition. When a beam of 1 nm X-rays fall incident on gold or some other metal at a shallow angle of 20 mrad, for example, the reflectance is on the order of several tens of percent. However, the large aberration that arises in the case of oblique incidence to a spherical surface again makes it impossible to obtain good focusing characteristics.
The Wolter-type optical system employing an ellipsoid of revolution and the Kirkpatrick-Baez-type optical system employing two perpendicularly intersecting elliptic cylinders were developed for mitigating this aberration problem. These oblique incidence optical systems can focus X-rays down to short wavelengths of around 0.08 nm. Aspheric surfaces are, however, difficult to fabricate with high precision.
Research has therefore been conducted for enabling spherical reflecting mirrors, which are relatively easy to fabricate with precision, to be used with normal incidence, which is advantageous from the point of aberration characteristics. Specifically, attempts have been made to take advantage of the fact that when a large number of interfaces are laminated at a fixed period, the intensifying effect produced by interference between the very weak X-ray waves reflected from the individual interfaces makes it possible to obtain a large reflectance notwithstanding the extremely small normal reflectances at the individual interfaces. This led to the development of multilayer X-ray reflecting mirrors consisting of a large number of laminated films each of a thickness approximately equal to one-quarter of the wavelength of the X-rays to be focused. Research into reflecting mirrors of this type has become particularly active since the development by T. Barbee et al. (Appl.Opt.24(1985)883) of a multilayer X-ray reflecting mirror with an unprecedented high reflectance of 65% with respect to 17 nm X-rays. Since this breakthrough, multilayer spherical reflecting mirror systems featuring imaging resolutions of several tens of nm have been developed. Among the advantages of these optical systems are that they can be built with diameters up to several tens of mm and that they permit relatively large converging angles of around 0.2 rad.
Separately from the foregoing, A. V. Baez (J.Opt.Soc.Am.42(1952)756) proposed a diffraction method for focusing X-rays by use of a Fresnel zone plate. The Fresnel zone plate has a large number of concentric ring-like openings spaced at prescribed intervals and decreasing in width toward the outside and can be used to focus X-rays by utilizing the interference between the diffracted X-rays from the individual rings. The size of the focal point is restricted by the width of the outermost ring and diffraction efficiency is less than 10%. Condenser zone plates of a diameter of 1 mm, an outermost ring width of 0.3 .mu.m and a focal distance of about 10 cm and microzone plates of a diameter of 20-plus .mu.m, an outermost ring width of 50 nm and a focal distance of about 0.6 mm are currently being produced. However, the converging angles of these plates is only several tens of mrad.
Still, no X-ray system capable of satisfactorily focusing X-rays of short wavelengths under 1 nm to a diameter of several .mu.m has yet been developed. Minute pinholes continue to be used. It is possible to produce a 0.04 nm X-ray microbeam or the like using a pinhole.
Although various X-ray focusing techniques have been developed as described in the foregoing, none is entirely satisfactory. Although some of these techniques have notable merits, they also have numerous drawbacks. Those that employ oblique incidence cannot be practically applied because of their large aberration. On the other hand, optical systems designed to mitigate this drawback by use of optical elements that are aspherical or have noncircular cross-sections, such as those of the Wolter-type and Kirkpatrick-Baez-type, are difficult to fabricate, especially when high precision is required.
It is also difficult to fabricate and achieve high precision in multilayer reflecting mirrors in the short wavelength region, even though they can use spherical optical elements and allow normal incidence, because of such stringent conditions as that the thickness of each layer has to be equal to one-quarter the wavelength of the X-rays to be focused as well as precisely constant and that the interfaces have to be clearly defined. It is in fact difficult to form multiple film layers at a short period so as to produce clearly defined interfaces with low surface roughness. As a result, an appreciable degree of reflectance can be achieved by normal incidence only at wavelengths of 4.4 nm or greater. Although X-rays with fairly short wavelengths can the focused by using oblique incidence, the method using oblique incidence is, as explained earlier, fundamentally undesirable. In other words, presently available multilayer X-ray reflecting mirrors provide high resolution when used for focusing X-rays of relatively long wavelengths of several tens of nm and longer, but are not suitable for focusing short wavelength X-rays.
Although the Fresnel zone plate described above can focus X-rays of shorter wavelength than can be focused with a multilayer optical system, it nevertheless does not perform well when the X-ray wavelength is too short, owing to the increase in X-ray penetration power with decreasing wavelength, and is therefore limited to applications at wavelengths down to, at best, 2-3 nm. Moreover, as was pointed out earlier, it has a low diffraction efficiency of around 10% and is not easy to fabricate.
In the method using a pinhole instead of an optical system, moreover, for X-rays in the high penetration power wavelength range the pinhole has to be formed in a substrate of considerable thickness. Since it is difficult to bore a pinhole with a large aspect ratio (ratio of thickness to diameter) with high precision, as well as for other reasons, it is not actually possible to form a pinhole with a submicrometer diameter. An even more fatal defect of this method is that almost all of the incident X-ray energy is cut off and goes to waste, so that the transmitted X-ray intensity is extremely low.
This invention was accomplished in light of the foregoing shortcomings of the prior art and aims at providing an X-ray refractive lens which enjoys an extended applicable wavelength range, provides good focusing performance, and is relatively easy to fabricate.
This invention was accomplished after the following considerations by the inventor:
(1) While a material having a concave shape of a paraboloid of revolution as indicated by the aforementioned Equation (3) is theoretically ideal as an X-ray lens, a piece of material with a spherical concave surface of radius R can approximate an X-ray lens having the focal distance f given by the aforementioned Equation (4) within a practical range. PA1 (2) The extent to which the focal distance f can be shortened merely by reducing the radius R has limits in terms of fabrication technology and practical use, and hence the focal distance f remains quite long even after maximum practical reduction. PA1 (3) The total focal distance f.sub.T can be reduced to f/N by cascading N X-ray lenses of long focal distance f, as shown in FIG. 1. In this configuration, however, many unit X-ray lenses have to be arranged after fabricating the individual unit X-ray lenses. The thickness of each unit X-ray lens has to be very thin to avoid strong absorption of X-rays, making each unit X-ray lens very fragile and difficult to handle. Moreover, aligning the optical axes of all unit X-ray lenses along the X-ray lens axis with high precision would be extremely difficult. Hence, arranging many X-ray lenses in the configuration shown in FIG. 1 is practically impossible.
For coping with the above problems, the inventor conceived the idea of disposing hollow hemispheres in a flat plate as shown in FIG. 2(a), in which X-rays enter from the side surface of the plate. The inventor further conceived the idea of disposing hollow cylinders instead of hemispheres for easier fabrication.
In the configurations shown in FIG. 2, all unit X-ray lenses can be fabricated in a single substrate, enabling the alignment of all X-ray lenses along the X-ray axis with high precision. Absorption of X-rays can be minimized by disposing the unit X-ray lenses very closely. Moreover, since hollow cylinders are very easy to bore, an X-ray lens composed of many hollow cylinders as shown in FIG. 2(b) can be fabricated very easily.
In the present invention, a unit X-ray lens made of a hollow cylinder or hollow hemisphere of radius R has a focal distance f.sub.U represented by EQU f.sub.U =R/2.delta. (5).
The reason for the focal distance f.sub.U represented by Equation (5) being half that of the focal distance f represented by Equation (4) is that the unit lens contains two concave surfaces along the X-ray axis indicated by the dashed lines in FIG. 2.
When N unit lenses are aligned, the effective focal distance F.sub.T with respect to a beam of X-rays entering the axis of the unit lens array, i.e., the X-ray lens axis, is EQU F.sub.T =f.sub.U /N (6).
For obtaining good focusing characteristics with a lens of this configuration, the machining has to be conducted at a high precision capable of keeping the geometric error within a small fraction of the value obtained by dividing the wavelength of the X-rays to be focused by .delta. of the lens material (=.lambda./.delta.). Even so, the machining precision required is far less stringent than that required for the fabrication of a prior art oblique incidence optical system, multilayer reflecting optical system, zone plate or the like. In addition, existing technologies are available for high-precision linear alignment of the N number of hollow cylinders or hollow hemispheres.